Abstract
This paper deals with the extension of the Donoho-Stark's uncertainty prin- ciple for the class of Fourier multiplier operators T-m := F-q(-1) (mF(q)) to time scale. Furthermore, the Bochner-Riesz mean operator, the Weierstrass transform and the Poisson integral are given using Fourier multiplier operators. Finally, the exact expression and some properties of the extremal functions of the so-called Tikhonov regularization problem are also determined; using reproducing kernel methods.